Finite Group Databasebeta

← #37583153

Subgroups — #37583153

Order 24448.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133284C211yesmaximal, characteristic, complemented
2#27133066C211yesmaximal, characteristic, complemented
3#27133045C211yesmaximal, characteristic, complemented
4#27133025C211yesmaximal, characteristic, complemented
5#27133022C211yesmaximal, characteristic, complemented
6#27132911C211yesmaximal, characteristic, complemented
7#27132907C211yesmaximal, characteristic, complemented
8#27132902C211yesmaximal, characteristic, complemented
9#27132897C211yesmaximal, characteristic
10#27132763C211yesmaximal, characteristic, complemented
11#27132761C211yesmaximal, characteristic, complemented
12C4×#15690277C211yesmaximal, characteristic, complemented
13C4×#15690272C211yesmaximal, characteristic, complemented
14#27132619C211yesmaximal, characteristic, complemented
15#542×C191C211yesmaximal, characteristic, complemented
16C2×#15690277C2211yescharacteristic
17C2×#15690275C2211yescharacteristic
18C2×#15690274C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690271C2211yescharacteristic
21C22×C191⋊C8C2211yescharacteristic
22#20259322C2211yescharacteristic
23#20259317—21no—
24#20259310C2211yescharacteristic
25#20259308—21no—
26#20259304—21no—
27#20259301C2211yescharacteristic
28#20259300—21no—
29#20259296C2211yescharacteristic
30C4×Dic382C2211yescharacteristic
31C4×D764C2211yescharacteristic
32#20259255C2211yescharacteristic
33#20259255C2211yescharacteristic
34#20259255C2211yescharacteristic
35#20259255C2211yescharacteristic
36#20259246C2211yescharacteristic
37#20259246C2211yescharacteristic
38#20259245C2211yescharacteristic
39#20259245C2211yescharacteristic
40#20259243C2211yescharacteristic
41#20259243C2211yescharacteristic
42#20259242C2211yescharacteristic
43#20259242C2211yescharacteristic
44#20259233C2211yescharacteristic
45#20259233C2211yescharacteristic
46C4×C191⋊C8C2211yescharacteristic
47C4×C191⋊C8C2211yescharacteristic
48C4⋊Q8×C191C2211yescharacteristic
49#126×C191—21no—
50#124×C191—21no—
51#124×C191C2211yescharacteristic
52#123×C191—21no—
53C22⋊Q8×C191—21no—
54C22⋊Q8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56C4×Q8×C191C2211yescharacteristic
57C4×D4×C191C2211yescharacteristic
58#117×C191C2211yescharacteristic
59C2×Dic382—21no—
60C2×Dic382C2311yescharacteristic
61C2×D764C2311yescharacteristic
62C2×C22⋊D191—21no—
63C2×C4×D191—21no—
64#15690277—22no—
65#15690275—22no—
66#15690274—22no—
67#15690272—22no—
68#15690271—22no—
69C2×C191⋊C8—22no—
70C2×C191⋊C8C2311yescharacteristic
71C2×C191⋊C8C2311yescharacteristic
72C2×C191⋊C8C2311yescharacteristic
73C2×C191⋊C8C2311yescharacteristic
74C4⋊Dic191—21no—
75C4⋊Dic191C2311yescharacteristic
76C4⋊Dic191C2311yescharacteristic
77Dic191⋊C4—21no—
78Dic191⋊C4—21no—
79C22⋊Dic191—21no—
80(C2×D191)⋊C4—21no—
81(C2×D191)⋊C4—21no—
82(C2×D191)⋊C4—21no—
83(C2×D191)⋊C4—21no—
84C4×Dic191—21no—
85C2×Q8×C191—21no—
86C2×Q8×C191C2311yescharacteristic
87C2×D4×C191—21no—
88C2×D4×C191C2311yescharacteristic
89C22×C4×C191—21no—
90C22×C4×C191C2311yescharacteristic
91C4⋊C4×C191—21no—
92C4⋊C4×C191—21no—
93C4⋊C4×C191—21no—
94C4⋊C4×C191D411yescharacteristic
95C4⋊C4×C191D411yescharacteristic
96C4⋊C4×C191C2311yescharacteristic
97C4⋊C4×C191C2311yescharacteristic
98C22⋊C4×C191—21no—
99C22⋊C4×C191—21no—
100C22⋊C4×C191—21no—
101C22⋊C4×C191—21no—
102C22⋊C4×C191—21no—
103C22⋊C4×C191D411yescharacteristic
104C22⋊C4×C191D411yescharacteristic
105C42×C191—21no—
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109Dic382—21no—
110Dic382—21no—
111Dic382—81no—
112D764—21no—
113D764—21no—
114C22⋊D191—81no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C4×D191—81no—
119C191⋊C8—21no—
120C191⋊C8—21no—
121C191⋊C8#4112yes—
122C191⋊C8#4112yes—
123C23×C191—21no—
124C23×C191C2×D411yescharacteristic
125Q8×C191—21no—
126Q8×C191—21no—
127Q8×C191—81no—
128D4×C191—21no—
129D4×C191—21no—
130D4×C191—81no—
131C2×C4×C191—21no—
132C2×C4×C191—21no—
133C2×C4×C191—21no—
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191—81no—
137C2×C4×C191C2×D411yescharacteristic
138C2×C4×C191C2×D411yescharacteristic
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2411yescharacteristic
143C22×C191—21no—
144C22×C191—21no—
145C22×C191—21no—
146C22×C191—41no—
147C22×C191—41no—
148C22×C191—41no—
149C22×C191C22×D411yescharacteristic
150C2×D191—41no—
151C2×D191—41no—
152C2×D191—41no—
153C4×C191—21no—
154C4×C191—21no—
155C4×C191—21no—
156C4×C191—21no—
157C4×C191—21no—
158C4×C191—41no—
159C4×C191—41no—
160C4×C191—41no—
161C4×C191C2×#4111yescharacteristic
162C4×C191C2×#4111yescharacteristic
163Dic191—41no—
164Dic191—41no—
165Dic191—41no—
166C2×C191—41no—
167C2×C191—81no—
168C2×C191#53211yescharacteristic
169C2×C191#57611yescharacteristic
170C2×C191#57811yescharacteristic
171D191—81no—
172C191#317511yescharacteristic, complemented, Sylow
173#3175—1911nomaximal, Sylow
174#542—1911no—
175#542D19111yescharacteristic, complemented
176#500—1911no—
177#495—1911no—
178#489—1911no—
179#489—1911no—
180#468—1911no—
181#468—1911no—
182#467—1911no—
183#466—1911no—
184#440—1911no—
185#440—1911no—
186C4×Q16—1911no—
187C4×D8—1911no—
188#405—1911no—
189C2×Q16—1911no—
190C2×SD16—1911no—
191C2×SD16—1911no—
192C2×D8—1911no—
193C2×M16—1911no—
194C22×C8—1911no—
195C4⋊Q8—1911no—
196C4⋊Q8C2×D19111yescharacteristic
197#126—21no—
198#126—3821no—
199#124—21no—
200#124—3821no—
201#124—1911no—
202#124C2×D19111yescharacteristic
203#123—21no—
204#123—3821no—
205C22⋊Q8—21no—
206C22⋊Q8—3821no—
207C22⋊Q8—1911no—
208C22⋊Q8C2×D19111yescharacteristic
209#121—1911no—
210#121C2×D19111yescharacteristic
211C4×Q8—1911no—
212C4×Q8C2×D19111yescharacteristic
213C4×D4—1911no—
214C4×D4C2×D19111yescharacteristic
215#117C2×D19111yescharacteristic
216#107—1911no—
217#107—1911no—
218#107—1911no—
219#107—1911no—
220#103—1911no—
221#103—1911no—
222#103—1911no—
223#103—1911no—
224#102—1911no—
225#102—1911no—
226#102—1911no—
227#102—1911no—
228#97—1911no—
229#97—1911no—
230C4×C8—1911no—
231C4×C8—1911no—
232C2×Q8—21no—
233C2×Q8—3821no—
234C2×Q8—1911no—
235C2×Q8C22×D19111yescharacteristic
236C2×D4—21no—
237C2×D4—3821no—
238C2×D4—1911no—
239C2×D4C22×D19111yescharacteristic
240C22×C4—21no—
241C22×C4—3821no—
242C22×C4C22×D19111yescharacteristic
243Q16—3822no—
244SD16—3822no—
245SD16—3822no—
246D8—3822no—
247M16—3822no—
248C2×C8—3822no—
249C2×C8—1911no—
250C2×C8—1911no—
251C2×C8—1911no—
252C2×C8—1911no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—3821no—
257C4⋊C4—3821no—
258C4⋊C4—3821no—
259C4⋊C4—1911no—
260C4⋊C4—1911no—
261C4⋊C4C22⋊D19111yescharacteristic
262C4⋊C4C22⋊D19111yescharacteristic
263C4⋊C4C22×D19111yescharacteristic
264C4⋊C4C22×D19111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—3821no—
271C22⋊C4—3821no—
272C22⋊C4—3821no—
273C22⋊C4—3821no—
274C22⋊C4—3821no—
275C22⋊C4C22⋊D19111yescharacteristic
276C22⋊C4C22⋊D19111yescharacteristic
277C42—21no—
278C42—3821no—
279C42C22×D19111yescharacteristic
280C42C22×D19111yescharacteristic
281C23—21no—
282C23—3821no—
283C23C2×C22⋊D19111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—3821no—
288Q8—3821no—
289Q8—15281no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—3821no—
294D4—3821no—
295D4—15281no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—3821no—
303C2×C4—3821no—
304C2×C4—3821no—
305C2×C4—15281no—
306C2×C4C2×C22⋊D19111yescharacteristic
307C2×C4C2×C22⋊D19111yescharacteristic
308C2×C4C2×C22⋊D19111yescharacteristic
309C2×C4C2×C22⋊D19111yescharacteristic
310C2×C4C2×C22⋊D19111yescharacteristic
311C2×C4C23×D19111yescharacteristic
312C8—3821no—
313C8—3821no—
314C8—1912no—
315C8—1912no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—7641no—
323C22—7641no—
324C22—7641no—
325C22C22×C22⋊D19111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—7641no—
335C4—7641no—
336C4—7641no—
337C4#41×D19111yescharacteristic
338C4#41×D19111yescharacteristic
339C2—41no—
340C2—81no—
341C2—15281no—
342C2#2713320911yescharacteristic
343C2#2713346611yescharacteristic
344C2#2713347811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#542×C191C2
socleC22×C191C22×D4
prime radical#27132897C2
hypercenter#542D191
hypocenterC191#3175
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #27133284C2semidirect
2. #27133066C2semidirect
3. #27133045C2semidirect
4. #27133025C2semidirect
5. #27133022C2semidirect
6. #27132911C2semidirect
7. #27132907C2semidirect
8. #27132902C2semidirect
10. #27132763C2semidirect
11. #27132761C2semidirect
12. C4×#15690277C2semidirect
13. C4×#15690272C2semidirect
14. #27132619C2semidirect
15. #542×C191C2semidirect
172. C191#3175semidirect
175. #542D191semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#271332842
#271330662
#271330452
#271330252
#271330222
#271329112
#271329072
#271329022
#271328972
#271327632
#271327612
C4×#156902772
C4×#156902722
#271326192
#542×C1912
#3175191